Correlation Coefficient:

Measures the linear relationship between 2 variables and it provides 2 pieces of information:
The Type of relationship (+/–) The Strength of relationship (0 ≤ r ≤ 1)

Causality:

A physical relationship where ‘x’ causes ‘y’

Usually proven by Experimental research – change one variable, record another variable, and try to hold all other variables constant (and a control) or: Or by Observational research – different values of one variable observed and a second variable recorded.

There may be a lurking variable (3rd variable)

Eg child shoe size and spelling ability

Just because two variables are correlated, does not mean that one of the variables is the cause of the other. It could be the case, but it does not necessarily follow:

There is a strong positive correlation between the number of cigarettes that one smokes a day and one's chances of contracting lung cancer (measured as the number of cases of lung cancer per hundred people who smoke a given number of cigarettes). The percentage of heavy smokers who contract lung cancer is higher than the percentage of light smokers who develop the disease, and both figures are higher than the percentage of non-smokers who get lung cancer. In this case, the cigarettes are definitely causing the cancer.

There is a strong negative correlation between the total number of skiing holidays that people book for any month of the year and the total amount of ice cream that supermarkets sell for that month. This means that the more skiing holidays that are booked, the less ice cream is sold. Is there a cause here? Are people spending so much money on ice cream that they can't afford skiing holidays? Is the fact that the ice cream is so cold putting people off skiing? Clearly not! The simple fact is that most people tend to book their skiing holidays in the winter, and they tend to buy ice cream in the summer.

Although a correlation between two variables doesn't mean that one of them causes the other, it can suggest a way of finding out what the true cause might be. There may be some underlying variable that is causing both of them. For instance, if a survey found that there is a correlation between the time that people spend watching television and the amount of crime that people commit, it could be because unemployed people tend to sit around watching the television, and that unemployed people are more likely to commit crime. If that were the case, then unemployment would be the true cause!